Effectiveness of smearing and tetrahedron methods: best practices in DFT codes

Density functional theory (DFT) codes are commonly treated as a "black box" in high-throughput screening of materials, with users opting for the default values of the input parameters. Often, non-experts may not sufficiently consider the effect of these parameters on prediction quality. In this work, we attempt to identify a robust set of parameters related to smearing and tetrahedron methods that return numerically accurate and efficient results for a wide variety of metallic systems. The effects of smearing and tetrahedron methods on the total energy, number of self-consistent field cycles, and forces on atoms are studied in two popular DFT codes: the Vienna Ab initio Simulation Package (VASP) and Quantum Espresso (QE). From nearly 40,000 computations, it is apparent that the optimal smearing depends on the system, smearing method, smearing parameter, and $k$-point density. The benefit of smearing is a minor reduction in the number of self-consistent field cycles, which is independent of the smearing method or parameter. A large smearing parameter -- what is considered large is system dependent -- leads to inaccurate total energies and forces. Bl\"ochl's tetrahedron method leads to small improvements in total energies. When treating diverse systems with the same input parameters, we suggest using as little smearing as possible due to the system dependence of smearing and the risk of selecting a parameter that gives inaccurate energies and forces.